Collision Avoidance for Convex Primitives via Differentiable Optimization Based High-Order Control Barrier Functions
Bibliographic record
Abstract
Ensuring the safety of dynamical systems is crucial, where collision avoidance is a primary concern. Recently, control barrier functions (CBFs) have emerged as an effective method to integrate safety constraints into control synthesis through optimization techniques. However, challenges persist when dealing with convex primitives and tasks requiring torque control, as well as the occurrence of unintended equilibria. This work addresses these challenges by introducing a high-order CBF (HOCBF) framework for collision avoidance among convex primitives. We transform nonconvex safety constraints into linear constraints by differentiable optimization and prove the high-order continuous differentiability. Then, we employ HOCBFs to accommodate torque control, enabling tasks involving forces or high dynamics. Additionally, we analyze the issue of spurious equilibria in high-order cases and propose a circulation mechanism to prevent the undesired equilibria on the boundary of the safe set. Finally, we validate our framework with three experiments on the Franka Research 3 robotic manipulator, demonstrating successful collision avoidance and the efficacy of the circulation mechanism.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".